An extremal composition operator on the Hardy space of the bidisk with small approximation numbers

JOURNAL OF APPROXIMATION THEORY

卷:252

Article

Li, Daniel^1,2  Queffelec, Herve^3,4  Rodriguez-Piazza, Luis^5,6 

[1] Univ Artois, Fac Jean Perrin, Lab Math Lens LML UR 2462, Rue Jean Souvraz,SP 18, F-62300 Lens, France

[2] Univ Artois, Fac Jean Perrin, Federat CNRS Nord Pas de Calais FR 2956, Rue Jean Souvraz,SP 18, F-62300 Lens, France

[3] Univ Lille Nord France, Lab Paul Painleve UMR CNRS 8524, USTL, F-59655 Villeneuve Dascq, France

[4] Univ Lille Nord France, Federat CNRS Nord Pas de Calais FR 2956, F-59655 Villeneuve Dascq, France

[5] Univ Seville, Dept Anal Matemat, Fac Matemat, Calle Tarfia S-N, Sevila 41012, Spain

[6] Univ Seville, IMUS, Calle Tarfia S-N, Sevila 41012, Spain

关键词: Approximation numbers;    Bidisk;    Composition operator;    Cusp map;    Distinguished boundary;    Hardy space;   

DOI  :  10.1016/j.jat.2019.105363

来源: Elsevier

【 摘 要 】

We construct an analytic self-map Phi of the bidisk D-2 whose image touches the distinguished boundary, but whose approximation numbers of the associated composition operator on H-2(D-2) are small in the sense that lim sup(n ->infinity)[a(n2)(C-Phi)](1/n) < 1. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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